As far as I know the only ways you could have everyone's name searchable on a decentralised federated system are either:
A central directory service, but that would require centralisation which is what the Fediverse is created to avoid. Someone might take the directory over.
or
Every server having all the details of everyone from every other server, but that would be prohibitively expensive and put people off starting servers. (Also, most of the data would never be used.)